Can You Solve the Frog Riddle?

In this riddle from TED-Ed, you're in a sticky situation. You're stranded in a rainforest and have accidentally eaten a poisonous mushroom. To survive the poison, you need to lick a very particular frog. But which frog is it?

You can watch the video below for more details, or read this description. The problem is simple: You are poisoned and you know that a particular species of frog produces the antidote, which will cure you if you lick it. But to make things more complex, you know that only female frogs of the species have the antidote—males do not. In this frog species, males and females look identical but males have a distinctive croak. (Males and females also occur in identical proportion in this species.) In one direction, you see a single frog. In another, a group of two frogs sitting together.

From the direction of the two frogs, you hear that distinctive "male frog" croak. Uh-oh! One of those two is definitely male.

As the poison sets in, you have to make a logical decision. You need to find a female frog with the antidote. Are your odds better going toward the group of two (one of which is definitely male), or toward the single unknown frog? And what are those odds, anyway?

Note that in this riddle you are not guaranteed to survive. You're just trying to take your best shot.

So which to choose, and why?

Watch the video below for a discussion of the problem and how the math stacks up behind one of the choices.

Make sure your head is in working order before trying to solve this riddle from TED-Ed, because it's a stumper.

Here's the scenario: You're an explorer who's just stumbled upon a trove of valuable coins in a remote dungeon. Each coin has a gold side and a silver side, each with an identical scorpion seal. The wizard who guards the coins agrees to let you have them, but he won't let you leave the room unless you separate the hoard into two piles with an equal number of coins with the silver side facing up in each. You've just counted the total number of silver-side-up coins—20—when the lights go out. In the dark, you have no way of knowing which half of a coin is silver and which half is gold. How do you divide the pile without looking at it?

As TED-Ed explains, the task is fairly easy to complete, no psychic powers required. All you need to do is remove any 20 coins from the pile at random and flip them over. No matter what combination of coins you choose, you will suddenly have a number of silver-side-up coins that's equal to whatever is left in the pile. If every coin you pulled was originally gold-side-up, flipping them would give you 20 more silver-side-up coins. If you chose 13 gold-side-up coins and seven of the silver-side coins, you'd be left with 13 silver coins in the first pile and 13 silver ones in your new stack after flipping it over.

The solution is simple, but the algebra behind it may take a little more effort to comprehend. For the full explanation and a bonus riddle, check out the video from TED-Ed below.

Angie Werner got a lot more than she bargained for on January 24, when she sat down to help her 8-year-old daughter, Ayla, with her math homework. As Pop Sugar reports, the confusion began when they got to the following word problem:

“There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”

Many people misread the problem and thought it was a trick question: if there are 36 more small dogs and the question is how many small dogs are competing, then maybe the answer is 36?

Wrong!

Frustrated by the confusing problem, Angie took to a private Facebook group to ask fellow moms to weigh in on the question, which led to even more confusion, including whether medium-sized dogs should somehow be accounted for. (No, they shouldn’t.) Another mom chimed in with an answer that she thought settled the debate:

"Y'all. A mom above figured it out. We were all wrong. If there is a total of 49 dogs and 36 of them are small dogs then there are 13 large dogs. That means 36 small dogs subtracted by 13 large dogs then there are 23 more small dogs than large dogs. 36-13=23. BOOM!!! WOW! Anyone saying there's half and medium dogs tho just no!"

It was a nice try, but incorrect. A few others came up with 42.5 dogs as the answer, with one woman explaining her method as follows: "49-36=13. 13/2=6.5. 36+6.5=42.5. That's how I did it in my head. Is that the right way to do it? Lol I haven't done math like this since I was in school!"

Though commenters understandably took issue with the .5 part of the answer—an 8-year-old is expected to calculate for a half-dog? What kind of dog show is this?—when Ayla’s teacher heard about the growing debate, she chimed in to confirm that 42.5 is indeed the answer, but that the blame in the confusion rested with the school. "The district worded it wrong,” said Angie. “The answer would be 42.5, though, if done at an age appropriate grade."